Find the mean of :(i) first eight natural numbers(ii) first six even n

1.	Find the mean of :(i) first eight natural numbers(ii) first six even natural numbers(iii) first five odd natural numbers(iv) all prime numbers upto 30(v) all prime numbers between 20 and 40.
Answer» (i) The first eight natural numbers are 1, 2, 3, 4, 5, 6, 7, 8 ∴ Sum of these observations =1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 and, number of their observations = 8 ∴ Required mean = 36/8 = 4.5 (ii) The first six even natural numbers are 1 = 2, 4, 6, 8, 10, 12 ∴Sum of these observations = 2, 4, 6, 8, 10, 12 = 42 and, number of their observations = 6 ∴ Required mean = 42/6 = 7 (iii) The first five odd natural numbers are = 1, 3, 5, 7, 9 ∴Sum of these observations =1 + 3 + 5 + 7 + 9 = 25 and, number of their observations = 5 ∴Required mean = 25/5 = 5 (iv) The all prime numbers upto 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ∴Sum of these observations = 2 + 3 +5 + 7+ 11 + 13 + 17 + 19 + 23 +29 = 129 and, number of their observations = 10 ∴ Required mean = 129/10= 12.9 (v) All prime numbers between 20 and 40 are 23, 29, 31, 37 Sum of these observations = 23 + 29 + 31 + 37 = 120 . and, number of their observations = 4 ∴ Required mean = 120/4 = 30

Find the mean of :(i) first eight natural numbers(ii) first six even natural numbers(iii) first five odd natural numbers(iv) all prime numbers upto 30(v) all prime numbers between 20 and 40.

Answer»

(i) The first eight natural numbers are 1, 2, 3, 4, 5, 6, 7, 8

∴ Sum of these observations =1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

and, number of their observations = 8

∴ Required mean = 36/8 = 4.5

(ii) The first six even natural numbers are 1 = 2, 4, 6, 8, 10, 12

∴Sum of these observations = 2, 4, 6, 8, 10, 12 = 42

and, number of their observations = 6

∴ Required mean = 42/6 = 7

(iii) The first five odd natural numbers are = 1, 3, 5, 7, 9

∴Sum of these observations =1 + 3 + 5 + 7 + 9 = 25

and, number of their observations = 5

∴Required mean = 25/5 = 5

(iv) The all prime numbers upto 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

∴Sum of these observations = 2 + 3 +5 + 7+ 11 + 13 + 17 + 19 + 23 +29 = 129

and, number of their observations = 10

∴ Required mean = 129/10= 12.9

(v) All prime numbers between 20 and 40 are 23, 29, 31, 37

Sum of these observations = 23 + 29 + 31 + 37 = 120 .

and, number of their observations = 4

∴ Required mean = 120/4 = 30